Hydrogeologists evaluated the hydraulic conductivity (K, in \text{m/day}) of four sediment… — ACT

Hydrogeologists evaluated the hydraulic conductivity ( $K$ , in $\text{m/day}$ ) of four sediment types under three compaction levels ( $1.4\text{ g/cm}^3$ , $1.6\text{ g/cm}^3$ , and $1.8\text{ g/cm}^3$ ). The results are presented in the following table:

Sediment Type	$K$ at $1.4\text{ g/cm}^3$ (m/day)	$K$ at $1.6\text{ g/cm}^3$ (m/day)	$K$ at $1.8\text{ g/cm}^3$ (m/day)
Clay	$0.002$	$0.001$	$0.0005$
Silt	$0.05$	$0.02$	$0.008$
Fine Sand	$4.5$	$2.1$	$0.9$
Coarse Gravel	$120.0$	$85.0$	$50.0$

Statement: If this data were translated into a line graph with compaction density on the horizontal axis and hydraulic conductivity ( $K$ ) on the vertical axis, the lines for all four sediment types would show a positive slope from left to right.

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The statement is False because higher compaction density leads to lower hydraulic conductivity for all four sediment types, which translates to a negative slope on a line graph.

The statement is incorrect because the tabular data shows an inverse relationship between compaction density and hydraulic conductivity (

K

). As compaction density increases from left to right along the table headers (

1.4 \rightarrow 1.6 \rightarrow 1.8\text{ g/cm}^3

), the corresponding

K

values decrease for all four sediment types. When translated into a line graph with density on the x-axis and

K

on the y-axis, lines that fall from left to right exhibit a negative slope, not a positive slope.

Adım Adım Çözüm

Identify the independent variable for the horizontal axis and the dependent variable for the vertical axis.

Compaction density (

1.4

1.6

1.8\text{ g/cm}^3

) is on the horizontal (

x

) axis, and hydraulic conductivity (

K

) is on the vertical (

y

) axis.

Establishing axis assignment is the first step in translating tabular data into graphical form.

Examine the trend of hydraulic conductivity (

K

) values as compaction density increases across each row.

For Clay (

0.002 \rightarrow 0.001 \rightarrow 0.0005

), Silt (

0.05 \rightarrow 0.02 \rightarrow 0.008

), Fine Sand (

4.5 \rightarrow 2.1 \rightarrow 0.9

), and Coarse Gravel (

120.0 \rightarrow 85.0 \rightarrow 50.0

K

consistently decreases as density increases.

Determining the direction of change in

y

relative to

x

reveals the graphical slope.

Translate the observed mathematical trend into a graphical feature (slope direction).

A relationship where

y

decreases as

x

increases forms a downward line from left to right, which defines a negative slope, making the claim of a positive slope false.

Translating inverse data trends to graphs requires correctly associating decreasing values with negative slopes.

Anahtar Kavram

Translating Tabular Relationships to Graphical Slopes

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